Introduction

The Ising model for a ferromagnet is not only a very simple model which has a phase transition, but it can also be used to describe phase transitions in a whole range of other physical systems. The model is defined using the equation

$$E = -\sum_{ij}J_{ij}\bi{S}_i\cdot\bi{S}_j$$ (4.27)

where the $i$ and $j$ designate points on a lattice and $\bi{S}$ takes the values $\pm{\mathchoice{{\textstyle{\frac12}}}{{\textstyle{\frac12}}}{{\scriptstyle{1/2}}}{{\scriptscriptstyle{1/2}}}}$. The various different physical systems differ in the definition and sign of the various $J_{ij}$'s.